I had a crown put in. It's sensitive to hot and cold. Should I give it more time?

Return to your Dr for an adjustment of the crown and further evaluation. A high spot on the crown or an opening at the margin of the crown or other can create much trauma to your tooth 

Sensitivity to temperature following a new crown cementation is not uncommon.  However your bite should feel normal.  Any premature hitting of the new crown against the opposing teeth may contribute to the sensitivity.  Check with your dentist and advise of this problem.  In addition, were you advised of the possibility that this tooth due to either decay or depth of previous filling, may need root canal?  Most dentists are conservative and if there is no actual sign of nerve involvement try to avoid the extra service and cost of the root canal for their patient.  But only mother nature knows for sure if it can be avoided.  So if pain, especially to hot persists, or swelling occurs, inspite of your dentist's best efforts you may need root canal.  This can be done either by tapping off the crown or in some cases accessing the tooth thru a small hole on the top that is later filled.  Your dentist will decide which is best.

It's a little too soon to say , but I think you need to get the bite checked on the crown. If the bite is too high it will cause cold and pressure sensitivity and on rare occasions, even heat sensitivity. Call your dentist.